I agree that "China" may mean several things but in the context of this discussion and previous comments it is rather clearer.
You can have a look at the Wikipedia link about the political status of Taiwan that @jacquesm posted. You can also have a look at related article about the history of China or Taiwan.
Quick summary (to mostly repeat myself as you point out but it does seem hard to get you guys to even read the links you provide yourselves, or don't want to accept them) is that China asserted control over Taiwan since the 17th century (as a reaction to European imperialism) with Taiwan acquiring province status towards the end of the 19th century. It was then ceded by China to Japan after the First Sino-Japanase war, and "reunited" in 1945. Following the Chinese civil war the communists took over the mainland and the government kept, and retreated to, Taiwan, which led to a split with de facto two states and official policies to "reunite".
That's all there in the links mentioned. So, again, I don't understand the drama.
I never denied that Taiwan was de facto a state independent of the mainland, or that the majority of the people of Taiwan do not want to be absorbed by the PRC, or even that a portion of the people of Taiwan would like no affiliation with "China" and be simply the Republic of Taiwan. And, yes, Taiwan was never controled by the PRC (like East Germany was never controled by West Germany prior to German "reunification", and there is still no country called "Germany" or "Korea"...). But that said I do have a problem with rewriting history and fallacious arguments to further a political aim.
